Poisson Distribution

Description

The Poisson Distribution models the number of times an event may occur in a set interval of time or space. So the probability of an event happening $k$ times in an interval where the average number of times this event happens $\lambda$ is

(1)
\begin{align} P(k)=e^{ -\lambda } \frac{ \lambda^{k} }{ k! } \end{align}

The Sage cell below gives the probability of an event happening 10 times in 100 tries, when the event will happen 15 tries on average.

Sage Cell

Code

lamb = 15
k = 10
P = exp( -lamb) * (( lamb^k ) / ( factorial(k) ))
numerical_approx( P )


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Tags

Primary Tags: Probability

Secondary Tags: Discrete Distributions: Poisson

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